However, the softmax classifier that JEM exploits is inherently discriminative, which may hinder its potential in image generation. To investigate this, we visualize the latent feature spaces learnt by a standard softmax classifier and by JEM through t-SNE [1]} in Figs. REF  and REF , respectively. Apparently, the feature space of the softmax classifier has been improved significantly by JEM as manifested by higher inter-class separability and intra-class compactness. However, JEM's latent space is not well formulated as probabilistic distributions, which may limit its generative performance and incur training instability as observed in [2]}. We hypothesize that generative classifiers (e.g., LDA) might be more suitable for image classification and generation. This is because generative classifiers model the data generation process explicitly with probabilistic distributions, such as mixture of Gaussians, which aligns well with the generative process of image synthesis. Therefore, in this paper we investigate an LDA classifier for image classification and generation. In particular, the Max-Mahalanobis Classifier (MMC) [3]}, a special case of LDA, fits our goal very well since MMC formulates the latent feature space explicitly as the Max-Mahalanobis distribution [4]}. Distinct to [3]}, we show that MMC can be trained discriminatively, generatively or jointly as an EBM. We term our algorithm Generative MMC (GMMC) given that it is a hybrid model for image classification and generation, while the original MMC [3]} is only for classification.
